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Unformatted text preview: ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Optical Resonator Modes ECE 455 Optical Electronics Tom Galvin Gary Eden ECE Illinois ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Introduction In this section, we will learn how to do the following things: ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B ABCD Matrix I The ABCD matrix is a ray optics formalism relates the distance r from the optical axis and its slope r of a ray as is propogates through optical elements. Assumptions ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B ABCD Matrix II Position above optic axis and slope are represented by a vector r r (1) Cummulative effect of optical elements are matrices A B C D (2) To find the position and slope of a ray after propogating through an optical system use r 2 r 2 = A B C D r 1 r 1 (3) ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B ABCD Matrix III Beware! Different books (notably Hecht and Siegman) use different conventions for ABCD matrices than defined in the previous page. Some switch the position of r and r . Another possible convention is to multiply the slope by the refractive index. ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Uniform Dielectric distance d Diagram d Axis ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Uniform Dielectric distance d It should should be clearly obvious that ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Thin Lens Diagram Axis ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Thin Lens The ABCD matrix of the thin lens can be derived as follows: ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Spherical Mirror Diagram r R = 2f f 1 2 ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Spherical Mirror The spherical mirror is identical to the case of a thin lens. Recall that the focus of a spherical mirror with radius R is f = R 2 (10) The result of the thin lens can then be used with the appropriate value substituted in place of f A B C D = 1 2 R 1 (11) ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Flat Mirror Consider the ABCD matrix of a spherical mirror....
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This note was uploaded on 02/28/2012 for the course ECE 455 taught by Professor Eden,j during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Eden,J

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